Question

23.a long straight wire in the horizontal plane carries a current of 50 Ain north to south direction.give the magnitude and direction of B at a point 2.5 m east of the wire?

Answer 1

Let d = perpendicular distance from Point P to the long wire.
         = 2.50 m given.

$\vec{dB}=\frac{\mu_0i}{4\pi}\frac{dl \times \hat{r}}{r^2}\\\\\vec{dB}\ has\ same\ direction\ \perp to\ diagram\ for\ all \ length\ of\ wire.\\\\dB=\frac{\mu_0i\ dl\ sin\theta}{4\pi r^2}.\ \ \ ---(1)\\\\l=-d\ cot\theta,\ \ dl=d\ cosec^2\theta d\theta\\r=d\ cosec\theta\\\\dB=\frac{\mu_0 i}{4 \pi d}sin\theta d\theta,\ \ \ ----(2)\\\\B=\frac{\mu_0 i}{4 \pi d}(Cos\theta_1 - Cos\theta_2)\ \ \ \ ----(3)\\\\For\ Long\ infinite\ straight\ wire:\\ .\ \ \ \ \theta_1=0,\ \ \theta_2=180^0\\\\B=\frac{\mu_0\ i}{2 \pi\ d}$

B = 2*10⁻⁷ * 50 /2.5  = 4 *10⁻⁶ Tesla